Practice Problem set ( Algorithms )

CMSC 104, Algorithms

Practice Problem Set ( Algorithms )

Definitions:

1.) An Algorithm is a finite set of unambiguous executable instructions that directs a terminating activity.

2.) A generic algorithm will work with any values for input. For example, any integer, any sentence, any set of numbers.

Problems:

First solve each of the following problems.
Then write an algorithm for each problem. Either English sentences OR pseudocode is acceptable.

A merchant wishes to mix peanuts costing $1.50 per pound with cashews costing $4.00 per pound, obtaining 50 pounds of a mixture costing $2.40 per pound. How many pounds of each type of nut should be used?

The algorithm should allow for changes in the costs of the peanuts and cashews.
The user should be specify the final weight of the purchase (50 lbs).

A store holding a clearance sale advertises that all prices have been discounted 20%. If a certain item is on sale for $28.00. , what was its price before the sale?

The algorithm should allow for the item to be at any sale price.

The algorithm should allow for any percent discount.

It costs a toy company ( 1000. + 2x ) dollars to manufacture x Big Bertha dolls. Each doll sells for $5.00 How many dolls must be sold to make $10,000 profit?

The algorithm should allow for different sale prices for the dolls
The user should be able to specify the amount of money to be made.

A student in a C programming course has test scores of 75, 82, 71, and 84. What score on the next test will raise the students average to 80? All tests are of equal value.

Allow the user to input different test scores
Allow the user to specify a different number of tests each time.

A newspaper boy has 125 coins, consisting of nickels and pennies. If the total amount is $4.25 how many coins of each type does he have?

The pressure acting at a certain depth in a liquid is directly proportional to the distance form the surface of the liquid to that depth. In a certain oil tank the pressure at a depth of 2 feet is 118 pounds per square foot. Find the pressure at a depth of 5 feet.

The algorithm should allow for different liquids. ie, different pressures of the liquid at a given depth.
The algorithm should allow for different depths to be measured.

A manufacturer sells a certain article to dealers at a rate of $20. each if less than 50 are ordered. If 50 or more are ordered, the price of each article is reduced 50 cents. What is the total cost of 100 units?

The algorithm should allow for changes in the $20 price, for purchases under 50 units.
The algorithm should allow for changes in the 50 cents reduced rate.